We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

China

Germany

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

We investigate the Klein-Gordon (KG) oscillators in a global monopole (GM) spacetime in Eddington-inspired Born-Infeld (EiBI) gravity and a Wu-Yang magnetic monopole (WYMM). We discuss the gravitational effects in the presence of Ricci scalar curvature <math altimg='si1.svg'><mi>R</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>&#965;</mi></mrow><mrow><mi>&#965;</mi></mrow></msubsup></math>. It is observed that the presence of the Ricci scalar curvature, effectively and manifestly, introduces a force field that makes the corresponding quantum mechanical repulsive core more repulsive. Similar effect is also observed for the EiBI-gravitational field. We reiterate and report that the corresponding bosonic KG-oscillator quantum mechanical system admits a solution in the form of confluent Heun functions, the truncation of which into a physically admissible polynomial is shown to be associated with some parametric correlations/conditions. The use of such conditions/correlations is mandatory and yields a set of allowed/restricted quantum mechanical orbital <italic>&#8467;</italic>-excitations, for all radial quantum numbers <math altimg='si2.svg'><msub><mrow><mi>n</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>&#8805;</mo><mn>0</mn></math>. Our procedure is shown to be quite handy, in the sense that it allows one to retrieve results for KG-oscillators in GM-spacetime in different EiBI-gravity and Ricci scalar curvature settings.

Türkiye

Omar Mustafa

KG-oscillators in Eddington-inspired Born-Infeld gravity: Wu-Yang magnetic monopole and Ricci scalar curvature effects

We consider Klein–Gordon (KG) particles in a global monopole (GM) spacetime within Eddington-inspired Born–Infeld gravity (EiBI-gravity) and in a Wu–Yang magnetic monopole (WYMM). We discuss a set of KG-oscillators in such spacetime settings. We propose a textbook power series expansion for the KG radial wave function that allows us to retrieve the exact energy levels for KG-oscillators in a GM spacetime and a WYMM without EiBI-gravity. We, moreover, report some conditionally exact, closed form, energy levels (through some parametric correlations) for KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity, and for massless KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity under the influence of a Coulomb plus linear Lorentz scalar potential. We report the effects of the Eddington parameter  $$\kappa $$  <math> <mi>κ</mi> </math>  , GM-parameter  $$\alpha $$  <math> <mi>α</mi> </math>  , WYMM strength  $$\sigma $$  <math> <mi>σ</mi> </math>  , KG-oscillators’ frequency  $$\Omega $$  <math> <mi>Ω</mi> </math>  , and the coupling parameters of the Coulomb plus linear Lorentz scalar potential, on the spectroscopic structure of the KG-oscillators at hand. Such effects are studied over a vast range of the radial quantum number  $$n_r\ge 0$$  <math> <mrow> <msub> <mi>n</mi> <mi>r</mi> </msub> <mo>≥</mo> <mn>0</mn> </mrow> </math>   and include energy levels clustering at  $$\kappa&gt;&gt;1$$  <math> <mrow> <mi>κ</mi> <mo>&gt;</mo> <mo>&gt;</mo> <mn>1</mn> </mrow> </math>   (i.e., extreme EiBI-gravity), and at  $$|\sigma |&gt;&gt;1$$  <math> <mrow> <mo>|</mo> <mi>σ</mi> <mo>|</mo> <mo>&gt;</mo> <mo>&gt;</mo> <mn>1</mn> </mrow> </math>   (i.e., extreme WYMM strength).

Brazil

A. Soares

C. Pereira

R. Vitória

On the Klein–Gordon oscillators in Eddington-inspired Born-Infeld gravity global monopole spacetime and a Wu–Yang magnetic monopole

The leading-order chiral Lagrangian for the baryon octet and decuplet states coupled to Goldstone bosons and external sources contains six low-energy constants. Five of them are fairly well-known from phenomenology, but the sixth one is practically unknown. This coupling constant provides the strength of the (p-wave) coupling of Goldstone bosons to decuplet states. Its size and even sign are under debate. Quark models and quantum chromodynamics (QCD) for a large number of colors provide predictions, but some recent phenomenological analyses even suggest an opposite sign for the Delta-pion coupling. The Goldberger-Treiman relation connects this coupling constant to the axial charge of the Delta baryon. This suggests a Wu-type experiment to determine the unknown low-energy constant. While this is not feasible in the Delta sector because of the large hadronic width of the Delta, there is a flavor symmetry related process that is accessible; the weak semileptonic decay of the Omega baryon to a spin <math><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math> cascade baryon. A broad research program is suggested that can pin down at least the rough size and the sign of the last unknown low-energy constant of the leading-order Lagrangian. It encompasses experimental measurements, in particular the forward-backward asymmetry of the semileptonic decay, together with a determination of the quark-mass dependences using lattice QCD for the narrow decuplet states and chiral perturbation theory to extrapolate to the Delta sector. Besides discussing the strategy of the research program, the present work provides a feasibility check based on a simple leading-order calculation.

Sweden

Magnus Bertilsson

Stefan Leupold

Goldberger-Treiman relation and Wu-type experiment in the decuplet sector

Scattering amplitudes in planar   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super Yang-Mills theory exhibit singularities which reflect various aspects of the cluster algebras associated to the Grassmannians Gr(4, n) and their tropical counterparts. Here we investigate the potential origins of such structures and examine the extent to which they can be recovered from the Gröbner structure of the underlying Plücker ideals, focussing on the Grassmannians corresponding to finite cluster algebras.

Mexico

L. Bossinger

United Kingdom

J. Drummond

R. Glew

Adjacency for scattering amplitudes from the Gröbner fan

Motivated by the latest discovery of a new tetraquark <math id="M2"><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math> with two charm quarks and two light antiquarks by LHCb Collaboration, we investigated the <math id="M3"><mi>D</mi><msup><mrow><mi>D</mi></mrow><mrow><mo>∗</mo></mrow></msup></math> hadronic molecule interpretation of <math id="M4"><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math>. By calculation, the mass and the decay width of this new structure <math id="M5"><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math> can be understood in one-meson exchange potential model. The binding energies for these <math id="M6"><mi>D</mi><msup><mrow><mi>D</mi></mrow><mrow><mo>∗</mo></mrow></msup></math> hadronic molecules with <math id="M7"><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup></math> are around 1 MeV. Besides, we also studied the possible beauty partners <math id="M8"><msub><mrow><mi>T</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow></msub><mfenced><mrow><mn>10598</mn></mrow></mfenced></math> of hadronic molecule <math id="M9"><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math>, which may be feasible in future LHCb experiments.

Ruilin Zhu

Huimin Ren

Fan Wu

Hadronic Molecule Interpretation of and Its Beauty Partners

We show that in an asymptotically flat space where an S-matrix can be defined, dual supertranslations leave all its matrix elements invariant and the Hilbert space of asymptotic states factorizes into distinct superselection sectors, labeled by their dual supertranslation charges. These results suggest that dual supertranslation may be interpreted as a redundant gauge symmetry of asymptotically flat spacetimes. This would allow to recast general relativity as a theory of diffeomorphisms possessing an additional asymptotic gauge symmetry. We then use the conjectured dual supertranslation gauge symmetry to construct a gravitational equivalent of the Wu-Yang monopole solution. The metric describing the solution is defined using two overlapping patches on the celestial sphere. The solution is regular on each one of the patches separately and differentiable in the overlap region, where the two descriptions are identical by virtue of a dual supertranslation gauge transformation. Our construction provides an alternative to Misner’s interpretation of the Taub-NUT metric. In particular, we find that using our approach, the Taub-NUT metric can be made regular everywhere on the celestial sphere and at the same time it is devoid of closed timelike curves, provided that the bound <math><mfrac><mi>m</mi><mo>ℓ</mo></mfrac><mo>≤</mo><msqrt><mfrac><mn>5</mn><mn>27</mn></mfrac></msqrt></math> on the ratio of mass to NUT charge is obeyed.

United States

Uri Kol

Massimo Porrati

Gravitational Wu-Yang monopoles

Within QCD reggeon field theory we study the formation of two subsequent triple pomeron vertices in the process P→PP→PPP. We make use of an earlier investigation [1] of the six-reggeon amplitude in deep inelastic scattering and show that in the large-N  c  limit pomeron fan diagrams emerge with the same triple pomeron vertex in all places. We thus confirm the BK-equation, but we also find additional terms related to the reggeization of the gluon, and we discuss their potential significance. Our analysis also includes the general pomeron → two odderon vertex: a particular version of this vertex has been included into earlier generalizations the BK equation.

J. Bartels

Russia

M. Braun

Pomeron fan diagrams in perturbative QCD

We construct a holographic superconductor model, based on a gravity theory, which exhibits novel metal-insulator transitions. We investigate the condition for the condensation of the scalar field over the parameter space, and then focus on the superconductivity over the insulating phase with a hard gap, which is supposed to be Mott-like. It turns out that the formation of the hard gap in the insulating phase benefits the superconductivity. This phenomenon is analogous to the fact that the pseudogap phase can promote the pre-pairing of electrons in high cuprates. We expect that this work can shed light on understanding the mechanism of high superconductivity from the holographic side.

Yi Ling

Peng Liu

Jian-Pin Wu

Meng-He Wu

Holographic superconductor on a novel insulatorSupported by Natural Science Foundation of China (11575195, 11775036, 11305018), Y.L. also acknowledges the support from Jiangxi young scientists (JingGang Star) program and 555 talent project of Jiangxi Province. J. P. Wu is also supported by Natural Science Foundation of Liaoning Province (201602013)

Wu black hole is the most general solution of maximally supersymmetric gauged supergravity in D=5, containing U(1) 3 gauge symmetry. We study the separability of the massless Klein-Gordon equation and probe its singularities for a general stationary, axisymmetric metric with orthogonal transitivity, and apply the results to the Wu black hole solution. We start with the zero azimuthal-angle eigenvalues in the scalar field Ansatz and find that the residuum of a pole in the radial equation is associated with the surface gravity calculated at this horizon. We then generalize our calculations to nonzero azimuthal eigenvalues and probing each horizon singularity, we show that the residua of the singularities for each horizon are in general associated with a specific combination of the surface gravity and the angular velocities at the associated horizon. It turns out that for the Wu black hole both the radial and angular equations are general Heun’s equations with four regular singularities.

Tolga Birkandan

Slovenia

Mirjam Cvetič

Wave equation for the Wu black hole